Question: Rewrite as a simplified fraction. ${0.\overline{75} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 75.7575...\\ 1x &= 0.7575...\end{align*}}$ Subtracting the two equations, we have: ${99x = 75}$ ${x = \dfrac{75}{99}} $ ${x = \dfrac{25}{33}} $